TAHA Engineering Toolsby TAHA Knowledge Lab

Energy & Renewables

Battery Bank Sizing Calculator

Battery capacity (Ah and kWh) and the series/parallel layout for your loads and days of autonomy.

Inputs

A battery bank of four batteries in series and three strings in parallel, connected to an inverter.VbVbVbVbVbVbVbVbVbVbVbVbNs in series → system voltage VNpstringsInverterη(inv), to AC loadsUsable = DoD × nominal energyC = E × days ÷ (DoD × k(T) × η(dis) × V)
Batteries in series (Ns) add up to the system voltage; parallel strings (Np) add capacity. Only part of the stored energy may be used (depth of discharge DoD), and cold, discharge and inverter losses take some more. C = E × days ÷ (DoD × k(T) × η(dis) × V). Diagram not to scale.

Energy used by appliances powered through the inverter.

Energy used by loads powered directly from the battery (DC lights, DC fridge…). 0 if none.

Applied to the AC loads only, from the inverter data sheet.

Applied to the DC loads only. 100% when DC loads run straight from the battery.

Share of the rated battery energy that actually leaves the terminals at your discharge rate (internal losses). From the data sheet; 100% if the rated capacity is already given at that rate.

How many days the battery must supply the loads without recharging.

From the battery data sheet for the cycle life you want. Often lower for lead-acid than for lithium batteries.

Capacity available at your lowest battery temperature, from the data sheet. 100% at the rated temperature.

Largest AC power drawn at one time, to check the discharge current.

Result

Energy leaving the battery terminals per day
4.80108
Nominal (rated) battery energy needed
12.0027
Required capacity at the system voltage
250.056Ah
Batteries in series per string
4in series
Parallel strings
3strings
Total batteries
12batteries
Installed (rated) energy
14.4
Usable energy at the terminals
11.52
Actual autonomy
2.399days
Working
E_terminal = 4 kWh ÷ 0.93 + 0.5 kWh ÷ 1 = 4.8011 kWh/day E_nominal = 4.8011 kWh × 2 ÷ (0.8 × 1 × 1) = 12.003 kWh C = 12,003 Wh ÷ 48 V = 250.06 Ah Layout: 4 in series × 3 strings = 12 batteries, 14.4 kWh rated, 11.52 kWh usable

The bank needs about 250.056 Ah at the system voltage: 12 batteries (4 in series × 3 strings), giving 2.399 days of autonomy.

  • Check the battery maker’s limits for charge and discharge rate (C-rate), temperature and, for lithium batteries, the battery management system.

Educational estimate — check the assumptions below.

About this calculator

This calculator sizes a battery bank so it can supply your loads for a chosen number of days without recharging. It keeps three energies separate: the energy used by the loads, the energy that must leave the battery terminals (after inverter and converter losses), and the rated battery energy needed once depth of discharge, temperature and discharge losses are allowed for.

It is the reverse of the Battery Runtime calculator, which shows how long a given battery lasts.

Formula

Eterm = EAC ÷ ηinv + EDC ÷ ηDC    Enom = Eterm × D ÷ (DoD × ktemp × ηdis)    C = Enom ÷ Vsys

Ns = Vsys ÷ Vbatt    Np = ⌈C ÷ Cbatt⌉    Eusable = Ns Np Vbatt Cbatt × DoD × ktemp × ηdis

The inverter efficiency applies only to AC loads, the DC-converter efficiency only to DC loads. Charging losses are not part of this sizing: they decide how much solar energy is needed to refill the battery (Solar PV System Sizing).

Worked example

AC loads 4.0 kWh/day through a 93% inverter, DC loads 0.5 kWh/day direct, discharge efficiency 95%, 2 days, 48 V, DoD 80%, temperature factor 95%, 12 V 100 Ah batteries:

  • Eterm = 4.0 ÷ 0.93 + 0.5 = 4.801 kWh/day
  • Enom = 4.801 × 2 ÷ (0.80 × 0.95 × 0.95) = 13.30 kWh → C = 13 299 ÷ 48 = 277.1 Ah (263.2 Ah with 100% discharge efficiency)
  • 4 in series × 3 strings = 12 batteries, 14.4 kWh rated, 10.40 kWh usable = 2.17 days.

Assumptions and limitations

  • Daily energy is the energy at the loads. Inverter efficiency is applied to AC loads only and DC-converter efficiency to DC loads only.
  • Battery capacity is the rated value at its standard discharge rate and temperature; the discharge-efficiency and temperature factors adjust it to your conditions.
  • Charging losses, self-discharge and ageing are not included in the size; allow for ageing with a lower allowed depth of discharge or a margin.
  • Series and parallel counts assume identical batteries. Follow the maker’s limits on parallel strings, charge rate and battery management.

References

  • Battery manufacturers’ data sheets (rated capacity, depth of discharge vs. cycle life, temperature and discharge-rate factors).
  • IEC 62548 and IEEE 1562 (sizing of stand-alone PV arrays and batteries) for detailed design.